Animation interaction with both hands
I'm guessing that what you are wanting is merely the two hands operating in concert to manipulate the paddle. If that is the case, then I can tell you that you don't need a rigid body for that, and in fact, it won't help you at all.
What you need are constraints. In particular, two IK constraints, one for each arm, each with its own independent target, and pole target, assigned (use newly created unparented bones to provide for these targets).
Then you will also likely need a Child Of constraint for each IK target bone, with the paddle object itself made the target of this constraint. You may also need either some tracking or copy rotation constraints to ensure that the hands don't wobble around and stay oriented properly.
Finally, you should have one final Child Of constraint on the paddle itself, with the target for that constraint put on the root bone of the character rig, so that the paddle will follow the character location when you move your entire rig.
With all this set up, you will be able to grab your paddle, move it, and even twist it, and your character's hands should stay stuck to it, and the arms move mostly correctly in response. You may have to occasionally adjust the pole targets for the arm IKs to get optimal positioning.